Randomness and Analytics of Die Rolls

[Weissrolf]

Then back to your question:

When you say useful what do you mean?

Useful in understanding/analyzing the result of FG's random number generator while the devs are not willing to share the underlying process (such as which RNG seed is being used).

[seycyrus]

Then back to your question:


Useful in understanding/analyzing the result of FG's random number generator while the devs are not willing to share the underlying process (such as which RNG seed is being used).

Why don't you just do a statistical analysis on a large number of rolls and then we can discuss your results to your hearts content.

[Weissrolf]

What are your thoughts on having a semi-automated way to build and display game statistics for each of your campaigns?

Yes, let's do that.

[seycyrus]

Yes, let's do that.

What are your answers to the other questions in that post?

[Weissrolf]

1. Yes.
2. No. Maybe half as much.

[damned]

I am in the process of (trying to) coding a MoreCore roll so people who like numbers can run some tests.
Its not working properly yet but i had it roll a d6 600x consecutively and this is what I got.

Plenty of 3 in a row - as best as I can tell there was a string of four 4s and nothing longer.
lowest number rolled was #3 with 86
highest number rolled was #2 with 108
6s outrolled 1s by the merest amount



600d6.jpg

[Weissrolf]

There is a row of 5 times rolled 4 in there.

Are you sure that these are 600 rolls and not 601? I just typed them all into Excel for calculations, but got an odd number. So before starting all over again, maybe your extension counts from 0 to 600 instead of 1 to 600? If not then I have to check all numbers again.

[Weissrolf]

I found the wrongly entered row and I am now in the process of manually typing the correct numbers back in (or rather shifting everything by one place).

[Weissrolf]

The data-size of 600 rolls is still too small, but here are the calculations I am more interested in than just averages.

Looking at two consecutive rolls as 2D6 we count 300 rolls with an expected and measured average of 7.

There is an average chance of 1/6 (16.67%) to roll a double with 2D6 (2 consecutive rolls), this corresponds to 50 out of 300 rolls.
There is an average chance of 1/36 (2.78%) to roll a specific double (1s, 2s, 3s, 4s, 5s, 6s), this corresponds to 8.3 out of 300 rolls.

Number of doubles rolled: 67

1s: 10
2s: 13
3s: 6
4s: 16
5s: 9
6s: 12

Ignoring the first and last roll shifts the results by 1 step (2nd + 3rd roll = 2d6 instead of 1st + 2nd roll). This creates a total of 298 rolls, the calculated average is 6.98.

Number of doubles rolled: 47

1s: 4
2s: 13
3s: 2
4s: 11
5s: 7
6s: 10

With a larger data-set (more rolls) the number of doubles should average towards 50 and the number of each specific double should trend towards 8.3. So we need more rolls and a way to automatically calculate these statistics, because I am not going to do it manually again, like never ever. :P

Another interesting metric would be the time distribution of numbers to see if we see patterns of ups and downs of averages. No use in knowing that the average over all numbers is 7 when we might get regular (patterns of) "locked" highs and lows. As with the doubles statistics above this is meant to reveal if rolls are affected by their predecessor rolls.

[Weissrolf]

Three anecdotes concerning computer generated random numbers:

- I once tested several tone/noise generators (software) running on the same Windows hardware. Only one Japanese program was able to create brown/pink/white noise being properly distributed over all frequency bands. One could feed dice results into a tone generator and easily measure the distribution (maybe even hear it when it's not as much noise as it should be).

- On the Commodore Amiga one could use the current position of the displays cathode ray as seed for RNG operations.

- The game "Little Computer People" allowed to enter a seed number that affected how the life of the little guy and his dog would unfold. Some Solitaire card games also allow to enter a seed number manually.